On the maximal spectrum of commutative semiprimitive rings

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The space of maximal ideals is studied on semiprimitive rings and reduced rings, and the relation between topological properties of Max(R) and algebric properties of the ring R are investigated. The socle of semiprimitive rings is characterized homologically, and it is shown that the socle is a direct sum of its localizations with respect to isolated maximal ideals. We observe that the Goldie dimension of a semiprimitive ring R is equal to the Suslin number of Max(R).

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@article{Samei2000, abstract = {The space of maximal ideals is studied on semiprimitive rings and reduced rings, and the relation between topological properties of Max(R) and algebric properties of the ring R are investigated. The socle of semiprimitive rings is characterized homologically, and it is shown that the socle is a direct sum of its localizations with respect to isolated maximal ideals. We observe that the Goldie dimension of a semiprimitive ring R is equal to the Suslin number of Max(R).}, author = {Samei, K.}, journal = {Colloquium Mathematicae}, keywords = {spectrum of a ring; maximal ideal space}, language = {eng}, number = {1}, pages = {5-13}, title = {On the maximal spectrum of commutative semiprimitive rings}, url = {http://eudml.org/doc/210774}, volume = {83}, year = {2000},}

TY - JOURAU - Samei, K.TI - On the maximal spectrum of commutative semiprimitive ringsJO - Colloquium MathematicaePY - 2000VL - 83IS - 1SP - 5EP - 13AB - The space of maximal ideals is studied on semiprimitive rings and reduced rings, and the relation between topological properties of Max(R) and algebric properties of the ring R are investigated. The socle of semiprimitive rings is characterized homologically, and it is shown that the socle is a direct sum of its localizations with respect to isolated maximal ideals. We observe that the Goldie dimension of a semiprimitive ring R is equal to the Suslin number of Max(R).LA - engKW - spectrum of a ring; maximal ideal spaceUR - http://eudml.org/doc/210774ER -